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Fungrim entry: a4ac32

1xdx=log ⁣(x)+C\int \frac{1}{x} \, dx = \log\!\left(\left|x\right|\right) + \mathcal{C}
Assumptions:xR{0}x \in \mathbb{R} \setminus \left\{0\right\}
TeX:
\int \frac{1}{x} \, dx = \log\!\left(\left|x\right|\right) + \mathcal{C}

x \in \mathbb{R} \setminus \left\{0\right\}
Definitions:
Fungrim symbol Notation Short description
RealIndefiniteIntegralEqualf ⁣(x)dx=g ⁣(x)+C\int f\!\left(x\right) \, dx = g\!\left(x\right) + \mathcal{C} Indefinite integral, real derivative
Loglog ⁣(z)\log\!\left(z\right) Natural logarithm
Absz\left|z\right| Absolute value
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("a4ac32"),
    Formula(RealIndefiniteIntegralEqual(Div(1, x), Log(Abs(x)), x)),
    Variables(x),
    Assumptions(Element(x, SetMinus(RR, Set(0)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-09-15 11:00:55.020619 UTC